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In figure given below, ∠PSR = 90°, PQ = 10 cm, QS = 6 cm and RQ = 9 cm. Calculate the length of PR.

In figure, ∠PSR = 90°, PQ = 10 cm, QS = 6 cm and RQ = 9 cm. Calculate the length of PR. Pythagoras Theorem, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Pythagoras Theorem

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Answer

In right angle △PQS,

By pythagoras theorem,

⇒ PQ2 = PS2 + QS2

⇒ 102 = PS2 + 62

⇒ PS2 = 102 - 62

⇒ PS2 = 100 - 36 = 64

⇒ PS = 64\sqrt{64} = 8 cm.

From figure,

RS = RQ + QS = 9 + 6 = 15 cm.

In right angle △PRS,

By pythagoras theorem,

⇒ PR2 = RS2 + PS2

⇒ PR2 = 152 + 82

⇒ PR2 = 225 + 64

⇒ PR2 = 289

⇒ PR = 289\sqrt{289} = 17 cm.

Hence, PR = 17 cm.

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